Q.Write the following interval in Set-Builder form: (-∞, 5].

An interval is a special subset of the real numbers R consisting of every real number lying between two fixed bounds, used constantly as a compact way to describe the solution set of an inequality. Six standard forms: open (a,b) — both endpoints excluded; closed [a,b] — both endpoints included; semi-closed [a,b) — left included, right excluded; semi-open (a,b] — left excluded, right included; and the two unbounded rays (a,∞)/[a,∞) and (-∞,b)/(-∞,b) — extending indefinitely in one direction, with ∞ and −∞ never themselves included (so the bracket beside infinity is always round). The full real line is R = (-∞,∞). Interval notation is essentially a shorthand for a set-builder description with an inequality, e.g. [6,12] = {x/x∈R, 6≤x≤12}. Bracket shape encodes inclusion precisely: a round bracket '(' or ')' means the endpoint is excluded (strict inequality <, >), while a square bracket '[' or ']' means the endpoint is included (non-stri …